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Centre of gravity , gravitational field intensity,shell theorem...? 1) centre of gavity of a body is a point at which weight of the body acts. 2)centre of gravity oy the body coincides with centre of mass if earth is assumed to have infinite radius. 3) to evaluate the gravitational field intensity due to any extended object its entire mass can be considered to be concentrated at its centre, which of the following statement(s) is true ? okay, lets start the discussion . while calculating gravitational force b/n a point mass and rod(mass M length L) with point mass placed at a distence d from end of rod, we found Fg = GMm/d(L+d) BUT, if we would have assumed mass of rod to be concentrated at its COM, Fg would have been GMm/(d+L/2)^2 so statement 3 is wrong. for statement 1, we should have bettter said COG is a point where weight of the body can be ASSUMED to act. statement 2 is true( i think) if earth is assumed to have infinite radius then g can be assumed to be constant and hence COG and COM coincides. I want u to elaborate each statement.

Centre of gravity , gravitational field intensity,shell theorem...?
1) centre of gavity of a body is a point at which weight of the body acts.
2)centre of gravity oy the body coincides with centre of mass if earth is assumed to have infinite radius.
3) to evaluate the gravitational field intensity due to any extended object its entire mass can be considered to be concentrated at its centre,
which of the following statement(s) is true ?
okay, lets start the discussion .
while calculating gravitational force b/n a point mass and rod(mass M length L) with point mass placed at a distence d from end of rod, we found Fg = GMm/d(L+d)
BUT, if we would have assumed mass of rod to be concentrated at its COM, Fg would have been GMm/(d+L/2)^2 so statement 3 is wrong.
for statement 1, we should have bettter said COG is a point where weight of the body can be ASSUMED to act.
statement 2 is true( i think) if earth is assumed to have infinite radius then g can be assumed to be constant and hence COG and COM coincides.
I want u to elaborate each statement.

Grade:12

1 Answers

Askiitians_Expert Yagyadutt
askIITians Faculty 74 Points
10 years ago

Hello  shubham....you have raised a very nice question...although ..few points in your discussion is quite correct and logical..but few need more light ...

 

# Center of mass is the point...where the whole mass of an object is assumed to be concentrated......A huge body of mass 300 Kg ..can be replaced by a point object placed at its COM of mass 300 ..to make question easier

 

# Center of gravity is the average location of the weight of the object...or simply what you are saying is assumed to be act ....

 

Now 1) If u consider more specific then this point has a bit uncertainity..but if u avoid it then it is correct

 

2) When gravitational field is uniform  then centre of gravity coincide with COM ..hence in case when R= infinte...gravitational force become uniform in all direction...so any object placed in such situation will have it COM and COG at same location

3) In third case you are absolutely currect....because in case of extended object mass is distributed uniformaly...so instead of considering COM you need an integration to calculate Force 

 

I hope this much ellaboration is fair enough

 

Cheers :D

With regards

Yagya

askiitians_expert

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